Using data from the California Strong Motion Instrumentation Program, we studied the relationship between building response and parameters describing the noxiousness of ground motion. According to vulnerability methods that use structural drift as damage criteria, we estimated the building response on the basis of the normalized relative roof displacement (NRRD), considered as damage criteria. The relationships between the NRRD and the intensity measures of the ground motion are developed using simulated annealing method. Grouping buildings by typology (defined according to their main construction material and height) reduces the variability of the building response. Furthermore, by combining IMs, the NRRD can be predicted more accurately by a Building Damage Prediction Equation. A functional form is thus proposed to estimate the NRRD for several building typologies, calibrated on the building responses recorded in California. This functional form can be used to obtain a fast and overall damage forecast after an earthquake.